Problem: Jimmy is trying to dive down and touch the bottom of the pool. The table below shows how far down he made it on each dive. Dive attempt Fraction of the distance to the pool bottom Dive $1$ $\dfrac13$ Dive $2$ $\dfrac35$ Dive $3$ $\dfrac56$ Jimmy's second dive was deeper than his first dive by what fraction of the pool?
Solution: To find the difference in the depths, we need to subtract. Distance to pool bottom $\frac{3}{5}$ $\frac{1}{3}$ Length of dive 2 Length of dive 1 Difference $\dfrac{3}{5}} - {\dfrac{1}{3}}$ Our denominators need to be the same so we can subtract What is the least common multiple for the denominators $5}$ and ${3}$ ? The least common multiple of $D5$ and ${3}$ is ${15}$. $\dfrac{3}\times3}{5}\times3} = \dfrac{9}{15}}$ $\dfrac{{1}\times5}{{3}\times5} = {\dfrac{5}{15}}$ Now, we can subtract our fractions. $\dfrac{9}{15}} - {\dfrac{5}{15}} = \dfrac{9} - {5}}{15} = {\dfrac{4}{15}}$ Jimmy's second dive was deeper by ${\dfrac{4}{15}}$ of the pool.